This application claims priority on Japanese Patent Application No. 10-9139/1997, filed Apr. 25, 1997, the entire diclosure which is incorporated herein by reference.
1. Technical Field
The present invention relates to a method of determining a shape error of a free-form surface.
2. Background Art
With respect to formings formed by press working such as the body of an automobile, discrepancy has been conventionally evaluated by experiences. That is, the free-form surface has been conventionally evaluated mainly by xe2x80x9cvisual observationxe2x80x9d. In recent years, however, designing using a computer (CAD) has been spread and a deformation upon processing can be simulated. Accordingly, means for evaluating a free-form surface, that is, for objectively defining discrepancy in a forming and displaying it is desired.
FIG. 1 shows a forming sample showing discrepancy in a plate forming. FIG. 2 is a diagram showing an example of a conventional method of evaluating a shape error in a free-form surface. The example relates to a result of numerical simulation using simulation software (ITAS-3D) reported in xe2x80x9cSimulation of 3-D sheet bending processxe2x80x9d (Takizawa et al., 1991, VD1 BERICHTE NR. 894), xe2x80x9cSome advances in FEM simulation of sheet metal forming processes using shell elementsxe2x80x9d (Kawka et al., 1995, Simulation of Materials Processing, Shen and Dawson (eds.), Balkema, Rotteerdam, pp. 735-740), and the like.
In FIG. 2, a white part shows a shape as a reference (for example, the shape of a die) and a mesh part indicates a shape obtained by a forming simulation. The reference shape and the simulation shape are displayed at the same position and only a part positioning on the front side is displayed. Consequently, a shape error between the simulation shape and the reference shape can be roughly determined from the displayed white and mesh parts. The method has, however, the following problems.
(1) It is necessary to determine a reference position and make the reference shape and the simulation shape accurately coincide with each other at the reference position. The result is largely influenced according to the way the reference position is determined.
(2) Since the position of the other part is largely displaced due to a partial bending, it is difficult to find the cause of occurrence of an error.
(3) How much the shapes coincide with each other as a whole cannot be shown by an objective numerical value.
FIG. 3 shows CMM data (about 40,300 points) measured by using a three coordinate measuring machine xe2x80x9cMitsutoyo Super BHN 506xe2x80x9d. FIG. 4 shows the top view of FIG. 3 (about 8,000 points). As shown in these figures, the shape of a forming item actually formed by using a die can be displayed as images as shown in FIGS. 3 and 4 by measuring the forming item by the three coordinate measuring machine. From the images, shape errors such as projected and recessed parts and a twisted part can be roughly determined from the views. The method, however, also has the above-mentioned problems (2) and (3) in the numerical simulation and has a problem that (4) when the reference shape is not flat but has a complicated curve, the difference from the result of the three coordinate measurement can be hardly determined.
As mentioned above, methods of experiment, measurement, and display of result for evaluating the shape error have not been systematized yet. There has not been a simple and clear definition as an index of a forming discrepancy and, further, an evaluation method which can be repeatedly performed has not been existed conventionally.
The present invention is made in order to solve the problems. That is, a principle object of the invention is to provide a method of determining a shape error of a free-form surface which can accurately grasp a different part between two three-dimensional shapes of an actual forming shape and a simulation shape by a computer simulation, a reference shape by CAD, or the like. It is another object of the invention to provide a method of determining a shape error of a free-form surface which can be applied without making the reference positions accurately coincide with each other, find the cause of occurrence of an error such as a partial bending, show how much the shapes coincide with each other as a whole by an objective numerical value, and easily determine the error even if the reference shape is complicated.
The inventors of the present invention have invented xe2x80x9cextended Gaussian curvaturexe2x80x9d as an evaluation model which does not depend on the coordinate system. According to the invention, a local shape error of a free-form surface is classified into three types (mountain, valley, and twist) by comparing an actual curved surface with, for example, a CAD curved surface as a reference. A method of calculating the ratio of the same labels by using the image processing technique has also been invented. The invention is based on the novel ideas.
According to the invention, there is provided a method of determining a shape error of a free-form surface by obtaining a principle curvature of a target curved surface Sxe2x80x2 and a principle curvature of a corresponding position of a reference surface S; and displaying each part by classifying it from the difference between the principle curvatures into (a) a case where the two principle curvatures increase, (b) a case where the two principle curvatures decrease, and (c) a case where one of the principle curvatures increases and the other decreases.
That is, according to a preferred method of the invention, xcex94xcexa1=xcexa1xe2x80x2xe2x88x92xcexa1, xcex94xcexa2=xcexa2xe2x80x2xe2x88x92xcexa2 are obtained from the principle curvature (xcexa1xe2x80x2, xcexa2xe2x80x2) of the target curved face Sxe2x80x2 and the principle curvature (xcexa1, xcexa2) of the reference curved face S. (1) When xcex94xcexa1xe2x89xa70 and xcex94xcexa2xe2x89xa70, (a) it is determined that the two curvatures increase. (2) When xcex94xcexa1xe2x89xa60 and xcex94xcexa2xe2x89xa60, (b) it is determined that two curvatures decrease. (3) When xcex94xcexa1xc2x7xcex94xcexa2 less than 0, (c) it is determined that one of the curvatures increases and the other decreases. Preferably, (a), (b), and (c) are determined as mountain, valley, and twist, respectively, and are displayed in different symbols or colors on an image. Further, it is preferable that the ratio of the same labels is calculated from the labels (a), (b), and (c) and is used as a coincidence ratio.
The Gaussian curvature K is a product xcexa1xcexa2 of the principle curvatures xcexa1 and xcexa2 of three-dimensional surfaces. (1) When K greater than 0, it is known that the shape is elliptic. (2) When K=0, it is known that the shape is parabolic. (3) When K less than 0, it is known that the shape is hyperbolic.
The invention relates to an extended Gaussian curvature. That is, according to the method of the invention, the principle curvature of a target curved surface Sxe2x80x2 including an error and the principle curvature of a corresponding position of a reference curved surface S are obtained and each part is classified into (a), (b), and (c) from the difference between the principle curvatures, namely, the parts can be displayed while being classified into the case where two principle curvatures increase, the case where two principle curvatures decrease, and the case where one of the principle curvatures increases and the other decreases. Thus, the different part between two three-dimensional shapes can be accurately grasped.
According to the method, the shape error can be determined by obtaining the principle curvatures of corresponding positions. Consequently, the invention can be applied without making the reference positions of two three-dimensional shapes accurately coincide with each other and the cause of occurrence of an error such as a partial bending can be found.
Further, by calculating the ratio of the same labels from the labels (a), (b), and (c) and using it as a coincidence ratio, how much the shapes coincide with each other as a whole can be grasped by an objective numerical value and an error can be easily determined even if the reference shape is complicated.
The other objects and advantageous features of the invention will be made clear from the following description with reference to the attached drawings.